Andrew Huddleston
Lab 4 - PH 255
1 Feb 2005
The Balmer Series in the Spectrum of Hydrogen
Purpose: The purpose of this experiment was to measure the spectral lines in the
Balmer series of hydrogen and then calculate the Rydberg constant. The
diffraction grading line spacing was determined initially by measuring the
diffraction angles of the emission lines of a mercury discharge lamp, and then
calculating D from the known wavelengths of the mercury spectral lines.
Equipment:
1. Mercury discharge lamp
2. Hydrogen discharge lamp
3. Grading spectrometer
Procedure:
The spectrometer was focused on the mercury discharge lamp and the diffraction
angle for each of the observed spectral lines was determined. From this data and
the known wavelengths of the spectral lines, the line spacing of the diffraction
grading was determined. (Alexander)
After the grading spacing was determined, the diffraction angles of the spectral
lines of a hydrogen discharge lamp were observed and the wavelengths were
determined. From this data a value for the Rydberg constant was determined.
(Alexander)
Equations:
N  D sin 
1
1
1
 R( 2  2 )

2
n
Where:
N=diffraction order, θ = diffraction angle, λ = wavelength, D = grating spacing, R
= Rydberg constant, n = energy level, (3, 4, 5, 6,…)
Data: see spreadsheet
Andrew Huddleston
Lab 4 - PH 255
1 Feb 2005
Sample Calculations:
D = λ/sinθ = 579.0 * 10E-9 / sin (17.6 deg) = 1.915E-6 m
λ = Dsinθ = 1.915E-7 * sin (23.5 deg) = 764 nm
1/764 nm = R(1/4 – 1/9), R = 1.097E-7 m -1
Results:
Average value of D = 1.74E-6
Hydrogen λ error:
Red: 692 nm, 5.5 % error
Blue: 506 nm, 4.1 % error
Violet: 448 nm, 9.3 % error
Rydberg error: 5.9 %
Error Analysis:
ΔD = -λcosθΔθ/sin2θ = -(579nm)(cos 17.6)(.01)/(sin2(17.6)
ΔD = 6.04E-8 m
ΔD/D = 6.04E-8 / 1.67E-6 = .036 = 3.63 %
Discussion:
Our calculated hydrogen wavelengths differed from the accepted values only
slightly, they were sufficient enough to render a Rydberg constant calculation of
less than 6 percent error of the accepted value. The calculations could have been
made more precise given the apparatus we were using could measure more
accurate angles. Overall the values calculated were sufficiently close given the
equipment we had and the amount of precision with which we measured our data.